Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The integration of a modified quick-sort algorithm for capacitor balancing in the MMC, supported by validation through Typhoon HIL, appears methodologically reasonable. However, the contribution falls short in positioning itself within the current state of the art, and the claimed novelty remains vague. The manuscript needs to clearly explain what sets this sorting approach apart, particularly regarding pivot selection and adaptive depth, and to quantify its computational advantages over standard algorithms. Without this, the reader is left uncertain about the real innovation.

The section describing the converter architecture is too detailed for a general audience and reads like a recap of standard material. It would benefit from a more concise treatment, especially if this is not central to the contribution.

Another point of confusion is how the pivot is dynamically selected in real time. The current explanation lacks clarity and needs to be expanded to aid understanding.

I also recommend the authors include details about the filter bandwidth and any latency introduced by the Typhoon HIL interface, as these are relevant for interpreting the simulation fidelity.

Several figures, specifically Figures 6, 10, and 12, are of notably poor quality. High resolution versions should be used, and it would improve the manuscript's visual coherence if font sizes in the figures matched the body text.

Regarding Table 3, more transparency is needed on how computation time was determined. Include platform specifications, timing methods, and system clock details to give readers confidence in the performance claims.

Finally, the paper would benefit from a discussion of possible integration hurdles in full-scale HVDC deployments. Addressing practical concerns would help bridge the gap between simulation and real-world implementation.

Author Response

We wish to express our sincere gratitude to the reviewer for their valuable and constructive comments, which have provided significant guidance in enhancing the quality of the manuscript.

Please see the attachment."

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Please see the attached.!!!

Comments for author File: Comments.pdf

Author Response

We wish to express our sincere gratitude to the reviewer for their valuable and constructive comments, which have provided significant guidance in enhancing the quality of the manuscript.

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The authors propose an innovative primary control strategy for a modular multilevel converter.

The proposed method utilizes interactive modelling tools, for real-time validation.

The results of the experimental activities validate the proposed method.

Some comments

The paragraph 2.2 Working Principle Of MMC needs to be completely revised. There are errors in the signs, in the symbols and the equations.

First, in the fig. 3 put Rl and Ll instead of Ru and Lu in the lower side of the leg.

Line 220: It is not clear why Ro is equal to Ru or Rl. There no reason to do that for a "symmetric converter design". I think that they are usually different (you do the same in the model of Thyphon HIL). The same for Lo

I think that the direction of Il if different from shown in fig.3. Otherwise, eq (2), (3), (4) are not valid.

Line:226: In fig. 3, eq (1) and (2) there is no representation of Idc. What is it? Is it Iac? And what is Io? In fig 3 it is represented as Iac

In eq (5), io has to be iac and the signs are negative, not positive

I n eq (6), io has to be iac. It is correct if Il versus is downwards, contrary to eq (2.3.4)

1. (7) I think that 2dt is dt. And you have pay attention to the versus of Il (review all the equations and figure 3)
2. (9) and (10) what is NC (what is C and N), L, idc?

Please review completely the paragraph.

Other comments

Fig. 7: which are the values of L1, L2, L3, R1, Vref of each capacitors? Ru and Rl are null and different by Ro?

Fig. 7. You show leg with three half-bridge modules. Which are the limits (in terms of number of modules) of Typhoon HIL?

Line 387: large numbers of submodules means? Give a number or do you have an idea about the limits?

The experimental setup is not clear. It seems that the experimental results are related to the setup made by Typhoon HIL and the TI interface card. It seems that the 3 level MMC prototype is not used. Or it is connected to the TI card  or to Thiphoon HIL or other microcontroller card? Typhoon is used to emulate the 3-level MMC? The mentioned PHIL (Power Hardware-in-the-Loop) is made by what?

The connections between the different devices and cards and the functionalities on them are non clear. Please, explain better the experimental setup.

Line 467: Which are the "traditional methods" used in the comparison? More than one?

Some corrections and typos

Line 70: in-dividual->individual

In some lines (84 and 91): hard-ware->hardware

Line 198-199: the sentence “Unlike the cascaded H-bridge converter, the half bridge MMC configuration does not require separate DC sources for each submodule” is not clear. Can you explain why and in which condition?

Line 234: figure 5-> figure 3

line 368: Figure X???

Author Response

We wish to express our sincere gratitude to the reviewer for their valuable and constructive comments, which have provided significant guidance in enhancing the quality of the manuscript.

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

Dear Authors:

Please read the attached file.

Kind regards

 

 

Comments for author File: Comments.pdf

Author Response

We wish to express our sincere gratitude to the reviewer for their valuable and constructive comments, which have provided significant guidance in enhancing the quality of the manuscript.

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Thank you for addressing the different points. I believe that a few things can still be improved: there is not a formal complexity analysis or comparison nor pseudocode or algorithm box that would let a reader reproduce the method. The latency/timing claims can be improved including the vendor spec.

But overall, in my opinion, the paper can be accepted.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

I thank the authors for the improvements about the description of the experimental setup.

A lot of errors remain in the “Mathematical Modelling Of The MMC”, even though the authors say they have made some changes, but they do not appear in the paper. I ask the author to pay attention to the equations and the figures.

Again, the paragraph 2.2 Working Principle Of MMC needs to be completely revised. There are errors in the signs, in the symbols and the equations.

I think that the direction of Il if different from shown in fig.3. Otherwise, eq (2), (3), (4) are not valid.

Eq 3: It is not clear why Icirc=1/2idc. I think that idc is equal to iu

Eq (6) is correct if Il versus is downwards, contrary to eq (2.3.4)

1. (7) I think that 2dt is dt. And you have pay attention to the versus of Il (review all the equations and figure 3)

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

Dear Authors:

The updated version of the manuscript shows that my comments and suggestions have been addressed and clarified, further improving the quality of the article. For my part, I have no further comments.

Best regards

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 3

Reviewer 3 Report

Comments and Suggestions for Authors

I do not understand why the authors do not try to review correctly the Mathematical Modelling Of The MMC.

Now, in this version eq (2), (3), (4), (6) are correct (the sign of il) only if the 𝒊𝒍 is defined positive downward in fig. 3.

In the "author response" the expression of iac and idc are different form the definitions of the paper.

The eq 7 is not correct: the term Vu-Vl has to be Vl-Vu; if Lu=Ll=Lo and Ru=Rl=Ro the term Ro(iu+il) becomes Ro/2(il-iu); there is no term Ro Iac etc. etc.

Review eq. 8.

Again, the paragraph 2.2 Working Principle Of MMC needs to be revised. There are errors in the signs, in the symbols and the equations. Do not use equations of other papers (like [37] or [14]), but try to use the classical laws by yourself.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 4

Reviewer 3 Report

Comments and Suggestions for Authors

I thank the authors for following the suggestions of the reviewers.